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Topic: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Replies: 8   Last Post: Mar 12, 2004 9:37 AM

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 Alexander Malkis Posts: 11 Registered: 12/13/04
Re: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Posted: Mar 10, 2004 3:38 PM
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1. the dimensions of A,X,Y should be compatible, in this case I think
they should be all square matrices.

2. If you require that AXA=AYA for all matrices A, then it would
certainly hold for A=identity matrix.

3. If A is some unknown matrix, i.e. then AXA=AYA tells you not much.
E.g. if A=[0]

Joenyim Kim wrote:
> Dear all,
>
> I wonder under what condition can I say X=Y if I have AXA=AYA?
>
> A is any matrix, not neccessarily square or non-singular... it can be
> rectangular and singular...
>
> Then can AXA=AYA reduce to X=Y?
>
> -------------------------------------
>
> I myself conceived that
>
> I can write AXA=AYA to be A(X-Y)A=0, since A is arbitarily any matrix, the
> only possible case is X=Y,
>
> am I right?
>
> Thanks a lot,
>
> -Joenyim
>
>

--
Best regards,
Alex.

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